Kadanoff Seminar - Entanglement entropy and edge modes in topological string theory, Gabriel Wong, Fudan University

Entanglement entropy and edge modes in topological string theory, Gabriel Wong, Fudan University

The Ryu Takayanagi formula identifies the area of boundary anchored extremal surfaces in AdS with the entanglement entropy of the boundary CFT. However the bulk microstate interpretation of the extremal area remains mysterious.  Progress along this direction requires understanding how to define entanglement entropy in the bulk closed string theory.   As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A model  in the context of Gopakumar Vafa duality.  We give a self consistent factorization of the closed string Hilbert space which leads to string edge modes  transforming under a q-deformed surface symmetry group.    Compatibility with this symmetry requires a  q-deformed definition of entanglement entropy.    Using the topological vertex formalism, we define the Hartle Hawking state for the resolved conifold and compute its q-deformed entropy directly from the closed string reduced density matrix.  We find a match with a target space replica calculation using the proposal of Susskind and Uglum.    We then apply the Gopakumar Vafa duality to  reproduce the closed string entropy from Chern Simons theory using the un-deformed definition of entanglement entropy.    Finally we relate non local aspects of our factorization map to analogous phenomenon recently found in JT gravity..